Find the Multiplier
Reading Graphs
Compound Interest
Word Problems
100
A function decreases by 20% every year. What is the multiplier?
0.80
100
Does this graph show exponential growth or decay?
decay
100
If a word problem talks about interest being compounded quarterly, how many times a year will it compound?
4 times per year
100
If a word problem says that a savings account earns interest each year, will the multiplier show growth or decay?
growth
because the value in the savings account is increasing through interest
200
A savings account earns 8% interest each year. What is the multiplier?
1.08
200
What is the starting value?
5
200
True or False: In general, the best compound interest rates are ones that compound more often.
True
200
An influencer starts a new tik tok trend that takes off and goes viral. On the first day he posts, his video gets 17,000 views. Every day after, the views on his video grow by 15%.
What is the multiplier?
Multiplier: 1.15
300
A function has a multiplier of 1.05. What is the percent increase each year?
5% increase
300
Which graph is growing at the fastest rate?
y = 10x
green line300
A small bookstore has 1,000 books and its collection grows by 2% each month. Which expression correctly represents the number of books the bookstore will have in 5 years?
(hint: How many months in a year?)
A. f(x) = 1,000(1.02)60
B. f(x) = 1,000(2)60
C. f(x) = 1,000(1.02)5
D. f(x) = 2(1,000)5
A. f(x) = 1,000(1.02)60
Starting value: 1,000
Multiplier: 1.02
exponent: 12 months x 5 years = 60
300
You start playing an open world survival video game that begins when a zombie strain infects an entire village with only 12 NPCs. Because this strain is so aggressive, the number of infected villagers grows by 80% every hour.
Find the following:
Initial value: ______
Multiplier: ______
Exponential Equation: p(t) = ________________
Starting value: 12
Multiplier: 1.8
Exponential Equation: p(t) = 12(1.8)t
400
A function has a multiplier of 0.85. What is the percent decrease each year?
15% decrease
400
What is the multiplier?
(hint: pick 2 points that are next to each other and divide the y values)
4
400
Ms. Kim had to take out a student loan for $20,000 that has an interest rate of 8% compounded semi annually.
Find the multiplier.
(hint: focus on what is in the parentheses)
Multiplier: 1.04
How to find it?
8% interest / 2 times compounded per year = 0.04
interest tells us exponential growth so 1 + 0.04 = 1.04
400
Students at Nathan Hale could not stop doing the 6-7 trend, especially in math class. One day, the teachers decided to start doing the trend too so that it would became lame and die out.
On the first day that teachers began doing the trend, 100 students were heard saying 6-7. Every day that they heard their teachers doing 6-7, the rate of students doing it dropped by 65%.
How many students were heard saying it after 3 days? Round to the nearest whole number.
Initial value: 100
Multiplier: 0.35
Exponential Equation: f(x) = 100(0.35)3
After 3 days, only 4 students were heard saying 6-7 at school.
500
The population of a city decreases by 0.5% each year. What is the multiplier?
0.995
500
Write an exponential equation based on the graph.
y = 1(4)x
500
A savings account earns 12% interest per year, compounded quarterly. You open an account and invest $50 on the first day.
What will the balance be after 2 years?
Starting value: 50
Multiplier: 12% interest / 4 times compounded = 3% --> turn into 1+0.03 = 1.03
Exponent: 4 times compounded x 2 years = 8
Equation: y = 50(1.03)8
After 2 years, the account will have $63.34.500
NYC has a huge rat problem, so in 2023 the city appointed the first ever Rat Czar to reduce the rat population over time. When the Rat Czar was appointed, city workers counted 750 rats in the downtown area. Every day after, the rat population decreased minimally by 5%. Write an equation to find out how many rats there will be after 2 weeks.
P(t) = _________________
P(t) = 750(0.95)14
Starting value: 750
Multiplier: (0.95)
exponent: 2 weeks x 7 days per week = 14